Examination of the Heat Transfer Model in Gas–Liquid–Solid Three Phases in Presence of Gas Hydrate Particle

Hydrate-based gas separation is often investigated using batch or semi-batch operations. To increase the throughput of the gas mixture without increasing the apparatus volume, it is preferable to perform a continuous operation of hydrate-based gas separation. Therefore, we proposed a flow-type apparatus for performing continuous formation with passing gaseous mixture and subsequently decomposition with passing gas hydrate particles. Characteristics of multiple fluid and heat and mass transfer of hydrate slurry are essential for the efficient operation of the apparatus. In this study, we focused on heat transfer characteristics in the presence of bubbles in water and surfactant solution. First, an apparent overall heat transfer coefficient under pressure during steady operation of the apparatus was calculated on a simple assumption. Next, to control the hydrate amount and position of hydrate-decomposition and hydrate-formation in the apparatus, we focused on the temperature profile of the inside fluid. A heat transfer model using heat balance of defining heat of hydrate-formation and heat transfer of agitation of fluid was made for hydrate-based gas separation apparatus. To evaluate the validity of the heat transfer model, a calculation value is compared with the experimental value.


Introduction
Gas hydrate is a non-stoichiometric crystal compound formed by the inclusion of gas molecules in the space of water molecules bound in a cage form by hydrogen bonding. Gas hydrate exists under low temperature and high pressure. There are many applied technologies of gas hydrate. In our laboratory, we are focusing on a hydrate-based gas separation in many applied technologies (Tajima et al., 2014). Hydrate-based gas separation is often investigated using batch or semibatch operations. To increase the throughput of the gas mixture without increasing the apparatus volume, it is preferable to perform a continuous operation of hydratebased gas separation. When gas hydrate formation for gas absorption and decomposition for gas stripping are carried out with a flow-type reactor, characteristics of multiple fluids (gas-liquid-solid phase) and heat and mass transfer are important information. However, there is little information about these characteristics yet. Therefore, we focused on heat transfer characteristics in the presence of bubbles and hydrate particles in water and surfactant solution. The aim of this study is to suggest a heat transfer model of hydrate slurry under the gas-liquid-solid three phases. Several heat transfer models by heat balances of the conditions as shown in Table1 were made and assessed based on assumptions for simplification. To evaluate the validity of the heat transfer model in the gas-liquid two phases, a calculation value was compared with the experimental value. We combined a hydrate-decomposition part with a hydrate-formation apparatus (Tajima et al., 2014) for continuous operation as shown in Figure 1. A staticmixer was set up in the hydrate-formation reactor because gas came in contact with liquid thoroughly. Pt residence thermometers were equipped at the top and the bottom of the hydrate-formation and the hydratedecomposition parts respectively. To keep the apparatuses at a constant temperature, those apparatuses were set up in separate low-temperature thermostats in which the air of forced convection in low-temperature thermostats cool those apparatuses.

Experimental operation
In order to produce gas hydrate, we used HCFC-22 (chlorodifluoromethane, R22) and nitrogen as test gases and ion-exchanged water. Water looped in the apparatus by using a pump. When water was cooled in the apparatus, the experimental temperature was set to 276 K or 278K at the hydrate-formation side and 286 K at the hydrate-decomposition side. Because the temperature in the center of the reactor equipped a static mixer kept the temperature of hydrate-formation or decomposition. Injected gas was contacted to water countercurrently. Experimental pressure in the apparatuses was set at 0.3MPa (An equilibrium temperature of HCFC-22 hydrate is 282.2 K at 0.291 MPa) (Javanmardi et al., 2004). To form hydrate slurry readily, the SDS solution (100ppm) was also tested instead of pure water. We measured the temperature at a steady state in the apparatuses in each condition.

Analysis method
To establish a heat transfer model fitted the hydrate formation apparatus, we took a step-by-step approach for the heat balance.

Estimation of overall heat transfer coefficient
To decide the overall heat transfer coefficient of the hydrate formation (static mixing) part, we measured the temperature at a steady state in the apparatuses with the water phase only. Temperature distribution in the apparatus was calculated by using forced convection heat transfer equation and heat balance. The average velocity of an air-cooling in the thermostats was estimated as a calculation value was equal to the experimental value. The overall heat transfer coefficient U was calculated using the following Equations (1)-(6).  ・The flow in the apparatus is the plug flow because a static-mixer is equipped in the apparatus.
・The thermal boundary layer inside the circular tube can be ignored.   The overall heat transfer coefficient was calculated without the gas. An average density of the fluid and an average specific heat of the fluid, an average of the volumetric flow of the fluid were calculated by the method similar to Section 2.2.2. An effective axial thermal conductivity was calculated by the following equation (Muroyama et al., 1978 When the gas velocity is high, EzL is equal to EzS. Therefore, kez was calculated in the condition of EzL＝ EzS. An axial dispersion coefficient of liquid was calculated by the following equation (Muroyama et al., 1978).   The overall heat transfer coefficient was calculated without the gas. An average density of the fluid and an average specific heat of the fluid, an average of the volumetric flow of the fluid were calculated by the method similar to Section 2.2.2.

Estimation of overall heat transfer coefficient
When the calculation value from Equations (1)-(6) was equal to the experimental value, the average velocity of air-cooling u was 2.68 m/s. This value is adequate as air-cooling velocity in a thermostatic chamber. Therefore, we used this value in this study. In this condition, gas hydrate cannot be formed and this is a gas-liquid two-phase case. When there was no back mixing, the temperature was decreased slightly and linearly. The temperature at Z=0.5 (gas inlet position) deviated from the experimental temperature. Therefore the model with back mixing for gas-liquid two-phase was tested according to Equation (12). However, the temperature calculated using the axial thermal conductivity kez calculated based on literature didn't approach the experimental result. When an axial thermal conductivity was changed to fit the experimental temperature, approximately 15-20 times higher value was obtained. This result implies that the actual mixing is harder than that of the calculated value of the effective axial thermal conductivity. This may be due to the mixing effect of a static mixer. It was suggested that it is necessary to reconsider the equation for calculating the effective axial thermal conductivity in the future. Using the fitted axial thermal conductivity, the temperature distribution at the bottom part (Z = 0.5m-0.35m) changed suddenly. The reason for this may be that the heat transfer by back mixing is larger than by the convective heat transfer. On the other hand, the change in the temperature at the upper part (Z = 0m ~ 0.35m) was slow. This result suggests that the convective heat transfer is larger than the heat transfer by back mixing in this part.

The temperature distribution in the reactor with the gas at atmospheric pressure
In the case of pressurized condition (0.3 MPa, 276K), the temperature distribution in the reactor denoted the same tendency of temperature at atmospheric pressure. The back mixing at pressurized condition was harder than that at atmospheric pressure because the number of the effective axial thermal conductivity at pressure is larger than that at atmospheric pressure. Figure 8 shows the temperature distribution in the reactor with hydrate. Also, in this case, the temperature distribution in the reactor denoted the same tendency of temperature change at various pressure conditions. The analysis result of Equation (11) overlapped with equation (7). This implied that the heat of formation of hydrate has little effect under this experimental condition (0.3 MPa, 278K).

Conclusion
We calculated the axial temperature distribution of hydrate formation reactor by several heat transfer models step-by-step. By using the temperature in the reactor without the gas, the average velocity of air-cooling and the overall heat transfer coefficient were obtained. The temperature distribution in the gas-liquid two-phase flow was calculated by the heat transfer model proposed. The results implied that the back mixing was harder at pressure than that at atmospheric pressure in this reactor. Further investigation and validation will be carried out for the temperature distribution under hydrate formation conditions.